Tangents and it...

The curve for which the slope of the tangent at any point is equal to the ratio of the abscissa to the ordinate of the point is :

The tangent to the curve $$ y=e^{2x} $$ at the point $$ (0,1) $$ meets x-axis at:

The equation of tangents to the curve $$ y(1+x^2 )=2-x, $$ where it crosses x-axis is:

The slope of tangent to the curve $$ x=t^2+3t-8,y=2t^2-2t-5 $$ at the point $$ (2,-1) $$ is:

The equation of the tangent to the curve $$y=1-e^{\dfrac{x}{2}}$$ at the point of intersection with $$Y-$$ axis 

The line $$5x-2y+4k=0$$ is tangent to $$4x^{2}-y^{2}=36$$, then k is:

If the tangent at $$(1,1)$$ on $$y^{2}=x(2-x)^{2}$$ meets the curve again at $$P$$, then $$P$$ is

The slope of the tangent to the curve $$x = t^{2} + 3 t - 8, y = 2t^{2} - 2t - 5$$ at the point $$(2, -1)$$ is

The normal at the point $$(1, 1)$$ on the curve $$2y + x^{2} - 3$$ is .............

The normal to the curve $$x^{2} = 4y$$ passing $$(1, 2)$$ is